2006 AIME I Problem 14

A tripod has three legs each of length 5 feet. When the tripod is set up, the angle between any pair of legs is equal to the angle between any other pair, and the top of the tripod is 4 feet from the ground. In setting up the tripod, the lower 1 foot of one leg breaks off. Let h be the height in feet of the top of the tripod from the ground when the broken tripod is set up. Then h can be written in the form \frac{m}{\sqrt{n}}, where m and n are positive integers and n is not divisible by the square of any prime. Find \lfloor m+\sqrt{n}\rfloor. (The notation \lfloor x\rfloor denotes the greatest integer that is less than or equal to x.)